This section provides sample calculations of system parameters including amplifier gain, output signal level, C/N ratio, and inter modulation distortion. Although these examples are presented simply, the design of any broadband system requires a great deal of care and RF signal distribution knowledge. Never attempt to design a large or complex system without first obtaining training or help from a qualified RF Systems Engineer. Usually, the design is performed by a qualified engineering contractor, or through the design services offered by the network equipment manufacturer.
Amplifier Gain
Amplifier gain is the one factor that allows the designer to overcome the loss caused by the coaxial cable. Usable gain is the amount of amplification the device can supply, less any flat loss associated with its internal modules, and less any reserve gain.
~ All signals on a single cable system pass through two diplex filters for each amplifier module encountered. The loss through an equalizer module is
proportional to the length of cable being equalized; 2 dB is an approximate figure to use in estimates.
~ Reserve gain is a small amount of amplifier gain set aside during the design process to accommodate signal level variations that can arise when implementing and using the network. This gain can be used when the length of an installed cable run exceeds the estimated value used for design calculations.
Amplifier Gain (Forward Path)
Minimum full gain (catalog specification) 26.5 dB
Diplex filter loss (2 x 0.6) 1.2 dB
Equalizer loss 2.0 dB
Reserve gain
Total loss 5.2 dB
Usable amplifier gain 21.3 dB
The distribution system will be designed with an amplifier gain of 21.3 dB in the forward path (the return path needs less gain, but the calculation is similar.
Amplifier Cascade
Amplifier cascade is the number of amplifiers connected in a series configuration (one after another) in a trunk system. Since each amplifier contributes some noise to the system, there is a practical limit to the maximum number of units that can be cascaded.
To determine the maximum cascade, several factors must be considered such as:
~ Output level of the amplifiers
~ System bandpass
~ The amount of cable loss between each amplifier
. In general, the more amplifiers in a cascade, the lower each amplifier's output level should be.
The following calculations show how to determine the minimum number of amplifiers needed to compensate for the signal loss of the longest cable run of a system. The amplifier cascade to use for designing the system (the design cascade) is then found by doubling this calculated minimum value (to provide room for expansion).
Amplifier Cascade
Longest cable run (estimated)
Cable loss (O.5-inch cable @ 300MHz) 1880 feet x 1.31 dBIlOO feet
Required cascade over longest run Cable loss / Usable gain
24.6 dB / 21.3 dB
Minimum required cascade Design cascade
2 x Minimum required cascade Amplifier Output Level
1880 feet 24.6 dB
1.1 amplifiers 2 amplifiers 4 amplifiers
Knowing the design cascade allows the calculation of the maximum amplifier output level permitted in that cascade. The amplifier's rated output level (the highest signal level it can deliver without exceeding distortion specifications) should be reduced by 3 dB for each doubling of the number of amplifiers in cascade.
Cascaded Amplifier OutP.llt Level 5c = 50 - 1000g(N)
where 5c = maximum permitted output level of each amplifier in cascade (dBm V) 50= rated output level of one amplifier (dBmV)
N = number of amplifiers in cascade
For example, using amplifiers whose rated output level is +48.0 dBmV, the permitted output level in a cascade of four units can be no more than 42 dBm V.
5c= 48 - 10l0g(4)
= 48 - 6
= 42 dBmV
Based on the above parameters and the design discussion, the sample system has the following design characteristics (table 5-3).
System Noise
Random noise occurs over a wide bandwidth and is associated with a network's amplifiers. Typical noise figures for amplifiers range from 7 to 11 dB. A previous section showed how the noise for a cascaded system can be calculated.
Noise can also be injected from outside sources such as radio transmitters and electrical motors. This type of noise is usually associated with specific frequencies or a particular frequency range.
Table 5-3.
Sample System Design Characteristics Single cable network, midsplit implemented Cable
Diameter 0.500 inches
Loss per 100 feet at 300 MHz 1.31 dB
Amplifier
Gain 21.3 dB
Output level +36.0 dBmV
Input level +14.7 dBmV
Minimum outlet level
across specified spectrum ( ± 1.5 dB) +6.0 dBmV When properly installed, the system should provide a noise floor 40 dB below the video carrier level. This means that the level of noise in the system should be 40 dB or more below the level of the nominal video carrier. When the noise floor is higher, an amplifier might be contributing more than its share of noise, or a portion of the distribution system might not be properly terminated.
Each amplifier contributes some noise to the system depending on its noise figure.
To determine if an amplifier is more noisy than it ought to be, the carrier-to-noise ratio of the system can be measured at various points to find the faulty device. This procedure is best done in a logical progression, either beginning at the headend or at the farthest point from the headend, and moving toward the opposite end until the fault has been isolated.
A specific type of noise found in many electrical systems is hum, which is noise at the ac power line frequency (60 Hz). The suggested limit for the carrier-to-hum (C/H) ratio for a full system is 40 dB or more. Cascading amplifiers in a system causes the system's C/H ratio to decrease by 6 dB for every doubling of the number of amplifiers.
The following example shows how the C/H ratio of a system is calculated, given a C/H ratio for each amplifier of -70 dB and a cascade of 20 amplifiers.
Carrier-to-Hum Ratio
Suggested limit > 40 dB
C/Hc = C/HO + 20l0g(N)
where C/Hc = C/H ratio of the cascaded system C/HO = C/H ratio of one amplifier
N = the number of amplifiers in cascade
For example,
C/Hc = -70
+
20log(20)= -70
+
26= -44 dB Intermodulation Distortion
Intermodulation distortion (IMD) occurs when desired signals on the system interact to produce undesired signals. The primary causes are amplifiers operating at improper levels and defective amplifier stages. Either of these situations might cause the unit to operate in a non-linear fashion, which can create IMD.
If Fl, F2, and F3 represent frequencies of carrier signals on the system, intermodulation distortion can occur at the following second-order beat frequencies:
~ Fl ± F2
~ Fl ± F3
~ F2 ± F3
Interference can also occur at the following third-order beat frequencies:
~ Fl ± F2 ± F3
The recommended limit on second-order inter modulation distortion is 60 dB below video carrier level. In a cascaded system, second-order beat frequency components increase by 6 dB for every doubling of the number of amplifiers in cascade. However, these same interference Signals decrease by 6 dB for every 3-dB drop in amplifier output level. As a result, lowering amplifier output level by 3 dB every time the cascade is doubled maintains the same second-order distortion specification.
This practice coincides with the recommendation of dropping amplifier output levels when cascading amplifiers to keep system noise levels within specifications.
Another measure of inter modulation distortion on the system is composite triple beat (CrB). CTB is caused by the combination of all possible third-order beat frequencies that occur on the system. Its source is nonlinear effects of system components on transmitted carrier signals. For example, if a system has five carrier signals at frequencies Fl, F2, F3, F4, and FS, the possible triple beats on the system are the follOWing.
~ Fl ± F2 ± F3
~ Fl ± F2 ± F4
~ Fl ± F2 ± FS
~ F2 ± F3 ± F4
~ F2 ± F3 ± FS
~ F3 ± F4 ± FS
The combination of all frequencies represented by these triple beat frequencies is the composite triple beat. The recommended limit for CTB is 51 dB or more below video carrier level. CTB increases by 6 dB with every doubling of the number of amplifiers in cascade.
Composite Triple Beat
CTBc = CTBO
+
20l0g (N)where CTBc = CTB ratio of a cascaded system CTBO
=
CTB ratio of one amplifierN = number of amplifiers in cascade The System Level Graph
A system level graph summarizes many of the design calculations for a broadband network in a graphical manner. This section discusses how such a graph can be made, and describes the sample shown in figure 5-7.
This graph shows the relationship between amplifier specifications (noise figure, rated output level) and system specifications (noise floor, carrier-to-noise ratio, distortion level, and amplifier cascade). It also shows the operating window inside which the amplifier's input and output levels must reside.
A graph like this can be used to check that amplifier operating levels are within acceptable ranges and to show what signal margins exist between the operating values and the limits. It can be generated with the following procedure.
1. Starting with a typical amplifier's noise figure (e.g., 8 dB), compute the equivalent noise input (ENI) for the system for cascades of 1, 2, 4,
8,
and 16 amplifiers. Plot the resulting values of ENI versus cascade.a. For a 75-ohm system with a 4-MHz bandwidth, the noise floor is -59 dBm V.
b. Adding a single amplifier with an 8 dB noise figure gives an ENI of -51 dBm V.
c. Each doubling of the number of amplifiers in cascade raises the ENI by 3 dB.
For example, with two amplifiers, the ENI moves up to -48 dBm V; with four amplifiers, it becomes -45 dBm V.
2. Select a signal-to-noise ratio for the system (e.g., 45 dB). Add this value to the plot of ENI versus cascade to obtain the plot of minimum acceptable input level.
3. Compute the maximum allowable output level for each value of cascade.
a. Find the rated output of a single amplifier for the desired distortion level from its specifications. This example uses a device with a rated output of
+
48 dBm V with a CTB of -57 dB.b. Plot output level versus cascade; the output level drops 3 dB with every doubling of the cascade to maintain the CTB specification.
4. The operating window for the system using these amplifiers is the area above the minimum input line and below the maximum output line.
5. Compute the maximum allowable gain for each cascade value by subtracting input from output. This value drops by 6 dB with each doubling of the cascade.
dB +54 ~~---r---.---r---r---'
MAXIMUM ALLOWABLE
~---r---r---~~~----_+---1 GAIN +30 ~---r---r---r---~~~~----1
+24 -r---r---_+---+---+---~~
dBmV +48 ~=---~---~---~---+---~
+42
+36
+30
+24
+18
+12
MAXIMUM AMPLIFIER OUTPUT FOR -57 dB COMPOSITE TRIPLE BEAT (CTB)
MINIMUM AMPLIFIER INPUT FOR +45 dB
+6 :;;.... ____ -1 SIGNAL·TO-NOISE RATIO
-3 -6
-36
+---t----+---+--+---t----::;:::ooo/
-t---r---r---;~:::oo' ... :;;....----_+----__i EQU IVALENT NOISE INPUT -r---r---~~~---+_----_+----__i(BASEDONAN8dB -48 +---~
__
t-==:::.----+---f_---_+----_l NOISE FIGURE) -5116 32
AMPLIFIER CASCADE
Figure 5-7. A Typical System Level Graph Using the System Level Graph
A graph developed with the preceding procedure can be used in several different ways. This section provides some ideas.
When designing the network layout, cable lengths cannot always be the desired length for amplifiers to be used at the exact design values. Once amplifier placement is
estimated, the loss for which it must compensate can be calculated, and the input level it sees can be found. Plotting this input level on the system level graph provides an estimate of its margin above the minimum input level.
If the calculated input level is below the minimum input level line, the system's SIN specification will not be met at that point in the distribution system, and the design must be modified to provide a higher signal level to this amplifier (e.g., shorten the distance between it and the previous amplifier).
After an adequate input level is delivered to the amplifier, its output level can be determined by adding the amplifier's gain to its input level. The output level should be below the maximum amplifier output level line on the graph; the difference between it and the maximum output value is the margin; 3 dB is commonly used as a minimum margin value.
If the output level is beyond the maximum amplifier output line, the design must be changed to avoid excessive distortion. Possible corrective measures include the following.
~ Decreasing the input signal level feeding the amplifier input level by introducing attenuators or by inserting more cable between it and the previous unit.
~ Lowering amplifier gain (but not too far, since trunk amplifiers operate best near their maximum level).
~ Using fewer amplifiers in cascade.